mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-28 07:21:07 +00:00
49 lines
1.3 KiB
Python
49 lines
1.3 KiB
Python
|
"""
|
||
|
|
LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them.
|
||
|
|
A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
|
||
|
|
Example:"abc", "abg" are subsequences of "abcdefgh".
|
||
|
|
"""
|
||
|
|
def LCS(x,y):
|
||
|
|
b=[[] for j in range(len(x)+1)]
|
||
|
|
c=[[] for i in range(len(x))]
|
||
|
|
for i in range(len(x)+1):
|
||
|
|
b[i].append(0)
|
||
|
|
for i in range(1,len(y)+1):
|
||
|
|
b[0].append(0)
|
||
|
|
for i in range(len(x)):
|
||
|
|
for j in range(len(y)):
|
||
|
|
if x[i]==y[j]:
|
||
|
|
b[i+1].append(b[i][j]+1)
|
||
|
|
c[i].append('/')
|
||
|
|
elif b[i][j+1]>=b[i+1][j]:
|
||
|
|
b[i+1].append(b[i][j+1])
|
||
|
|
c[i].append('|')
|
||
|
|
else :
|
||
|
|
b[i+1].append(b[i+1][j])
|
||
|
|
c[i].append('-')
|
||
|
|
return b,c
|
||
|
|
|
||
|
|
|
||
|
|
def print_lcs(x,c,n,m):
|
||
|
|
n,m=n-1,m-1
|
||
|
|
ans=[]
|
||
|
|
while n>=0 and m>=0:
|
||
|
|
if c[n][m]=='/':
|
||
|
|
ans.append(x[n])
|
||
|
|
n,m=n-1,m-1
|
||
|
|
elif c[n][m]=='|':
|
||
|
|
n=n-1
|
||
|
|
else:
|
||
|
|
m=m-1
|
||
|
|
ans=ans[::-1]
|
||
|
|
return ans
|
||
|
|
|
||
|
|
|
||
|
|
if __name__=='__main__':
|
||
|
|
x=['a','b','c','b','d','a','b']
|
||
|
|
y=['b','d','c','a','b','a']
|
||
|
|
b,c=LCS(x,y)
|
||
|
|
print('Given \nX : ',x)
|
||
|
|
print('Y : ',y)
|
||
|
|
print('LCS : ',print_lcs(x,c,len(x),len(y)))
|